The present invention relates to a sensor and method for determining the attitude of vehicles, including aircraft and spacecraft, using the Global Positioning System (GPS).
The Global Positioning System (GPS) constellation was originally developed to give a wide variety of user vehicles an accurate means of determining position for autonomous navigation. The constellation includes 24 space vehicles (SVs) in semi-synchronous (12 hour) orbits, providing a minimum of six SVs in view for ground-based navigation. The underlying principle involves geometric triangulation with the GPS SVs as known reference points to determine the user""s position to a high degree of accuracy. The GPS was originally intended for ground-based and aviation applications, gaining much attention in the commercial community (e.g., automobile navigation, aircraft landing, etc.). However, in recent years there has been a growing interest in space-based applications. Since the GPS SVs are in approximately 20,000 km circular orbits, the position of any potential user below the constellation may be easily determined. A minimum of four SVs are required so that in addition to the three-dimensional position of the user, the time of the solution can be determined and in turn employed to correct the user""s clock.
Since its original inception, there have been many innovative improvements to the accuracy of the GPS determined position. These include using local area as well as wide area differential GPS, so-called xe2x80x9cpseudolitesxe2x80x9d (ground-based GPS transmitters), and carrier-phase differential GPS. In particular, carrier-phase differential GPS measures the phase of the GPS carrier relative to the phase at a reference site, which dramatically improves the position accuracy. Also, for spacecraft applications dynamically aided GPS using orbit models with GPS measurements in an extended Kalman filter can improve position accuracy.
Early applications of this concept to user spacecraft in Low Earth Orbits (LEOs) have demonstrated extremely useful results. Recently, there have been investigations of position determination by user spacecraft from above the GPS constellation. However, since current GPS SVs transmit their signals towards the Earth, this concept poses a much more difficult problem because the user spacecraft must rely on xe2x80x9cspillagexe2x80x9d signals received from GPS SVs on the far side of the Earth.
Another aspect of space-based applications using GPS that has gained much recent attention is attitude determination. One of the first space-based applications was flown on the RADCAL (RADar CALibration) spacecraft, which demonstrated a GPS attitude determination capability using post-processed measurements. To obtain maximum GPS visibility, and to reduce signal interference due to multipath reflection, GPS patch antennas were placed on the top surface of the spacecraft bus. Although the antenna baselines were relatively short for attitude determination (0.67 meter separation), attitude accuracy on the order of 2 degrees per axis (3"sgr") was achieved. Another experiment, Crista-SPAS provided the first on-orbit demonstration of real-time attitude determination. The spacecraft contained an accurate gyro reference, but the coordinate frame alignment was not measured relative to the GPS attitude reference frame, which means that discrepancies between the two reference frames might account for slightly different measurements from the two systems. Over the course of the experiment, the two sets of attitude solutions agreed to within 2 degrees, which was thought to be within the alignment tolerance of the two reference frames. The first extended real-time GPS based attitude determination mission was flown on the REX-II spacecraft, which tested actual attitude control using GPS attitude measurements.
The differential carrier-phase measurement error has a standard deviation of about 10 degrees, a small fraction of the standard wavelength. However, many error sources can significantly contribute to attitude inaccuracy. These include: reflections of the GPS carrier from the environment surrounding the antennas (multipath), electrical dissipation inherent when passing carrier-phase signals over the lengths of the RF cables between antennas and receiver (line bias errors), antenna motions due to external disturbances (e.g., thermal distortion effects), constellation availability, tropospheric refraction, and cross-talk errors. The most significant error source and the most difficult to overcome is multipath. In fact, multipath effects can be so pronounced as to be a major driver for the location of the GPS antennas on a vehicle. Despite limited successes with recent attempts at modeling multipath, this error remains a limiting factor in the performance of carrier-phase based GPS attitude determination. This is due to the complex physical nature of the reflecting surfaces, which depends mostly on antenna locations. Line biases can also adversely affect carrier-phase based attitude. These biases are typically determined by performing extensive calibrations (self survey) of the flight system on the ground prior to launch. However, since the space environment can significantly alter the physical properties of the cable through large temperature gradients, a permanent solution to this problem remains elusive. Yet another error source for the carrier-phase based method involves shifting baselines. In general, the attainable attitude accuracy improves with longer baselines. If, however, satisfactorily separating the GPS antennas requires mounting them on flexible structures (such as solar arrays, or deployable booms), then the attitude performance of the carrier-phase based method can be seriously compromised to the point where the advantages of the longer baseline is compromised. It is important to recognize that the aforementioned errors are primarily a result of the physical problems associated with using carrier-phase based measurements for attitude determination.
Before the actual GPS attitude determination can be performed, the correct number of integer wavelengths between each pair of antennas must be found. The resolution of these integer ambiguities has been extensively investigated. Such integer resolution techniques fall into two general categories: instantaneous and motion-based techniques. Instantaneous techniques provide immediate integer resolution without vehicle motion; however, the uniqueness of the solution may be severely degraded with sensor noise. Motion-based techniques use a batch of data to determine the integers; however, they rely on sufficient vehicle motion to obtain system observability. In either case, it is essential that these integers are accurately resolved before attitude determination can occur.
In accordance with the present invention, a GPS system for navigation and attitude determination is provided, comprising a sensor array including a convex hemispherical mounting structure having a plurality of mounting surfaces, and a plurality of antennas mounted to said mounting surfaces for receiving signals from space vehicles of a GPS constellation; and a receiver for collecting said signals and computing said navigation and attitude determination.
In accordance with another aspect of the present invention, a GPS sensor for navigation and attitude determination is provided, comprising two opposing convex hemispherical mounting structures, each of said mounting structures having a plurality of mounting surfaces, and a plurality of antennas mounted to said mounting surfaces.
In accordance with another aspect of the present invention, a GPS sensor array for navigation and attitude determination is provided, comprising a convex hemispherical mounting structure having a plurality of antenna mounting surfaces, said convex hemispherical mounting structure; and a plurality of antenna elements, each mounted to one of said mounting surfaces of said hemispherical mounting structure, wherein each of said plurality of antenna elements has a restricted field-of-view, said restricted field-of-views being oriented in a predetermined configuration to maximize the accuracy of said navigation and attitude determination.
In accordance with another aspect of the present invention, a method of determining the attitude of a vehicle is provided, comprising receiving a plurality of GPS carrier signals from a plurality of GPS space vehicles into a sensor array having a plurality of antenna elements, each having a restricted field-of-view; and polling each antenna element of said sensor array to determine which of said GPS space vehicles are within said restricted field-of-view of each antenna element; and constructing and minimizing a loss function to determine said attitude.
In accordance with another aspect of the present invention, a method of determining the navigation and attitude of a vehicle is provided, comprising receiving a plurality of GPS carrier signals from a plurality of GPS space vehicles using a sensor array having a plurality of antenna elements, each having a restricted field-of-view; and computing a navigation and attitude by determining which of said space vehicles is within said restricted field-of-view of each of said antenna elements.
In accordance with another aspect of the present invention, a method of determining the navigation and attitude of a vehicle using a plurality of GPS carrier signals from a plurality of GPS space vehicles collected by a sensor array having a plurality of antenna elements, each having a restricted field-of-view is provided, comprising determining which of said GPS spacecraft are within said restricted field-of-views; forming sightline vectors and determining optimal weighting using area formulas; determining said attitude by minimizing a loss function; mapping said sightline vectors into a body frame; determining an angle between said mapped sightline vectors and said boresights; determining whether each said mapped sightline vector is outside of its corresponding restricted field-of-view; and repeating the recited steps until each of said mapped sightline vectors is within its corresponding restricted field-of-view.
This new approach involves using an array of GPS antenna positioned to provide maximum sky coverage. This array is used only to find which GPS spacecraft are within the field-of-view (FOV) of each antenna. Attitude determination is performed by considering the sightline vectors of the found GPS spacecraft together with the boresight vector of the particular antenna, unlike interferometric methods. The boresight is used since the exact location of the GPS spacecraft in the body-frame of the antenna FOV is not known. The approach is similar to a star tracker, with the GPS sightline vectors as the inertial reference vectors and the antenna boresight vectors as the body vectors. Multiple antennas are used to increase attitude accuracy.
The advantages of the new sensor approach include: 1) differential carrier-phase measurements are not required, 2) attitude errors from multipath can be reduced or even eliminated, 3) integer ambiguities do not need to be resolved, and 4) line biases do not need to be determined. Therefore, the new sensor approach is easy to implement and use for any application. It will be shown that the accuracy of the new sensor is better as the FOV decreases.
Multiple sensor configurations were tested to investigate this phenomenon. Accuracies were obtained that prove that the CEGANS concept can meet the attitude requirements of a wide variety of vehicles. In addition, as technology evolves and GPS receivers and antennas become more and more capable, this method can be further refined by better processing schemes and an increase in the number of antenna elements. This potential is in stark contrast to the potential for growth inherent in differential or carrier-phased base methods of comparable capability, which are asymptotically approaching the limits imposed by physics.